# How do you find the roots, real and imaginary, of y= -2(x+1)^2+(-x-2)^2  using the quadratic formula?

Jan 5, 2016

Form a quadratic equation, and solve it. Method below first, solution underneath.

#### Explanation:

Method

Start by writing your equation in the form:
$y = a {x}^{2} + b x + c$

The roots are when $y = 0$
So you will have a quadratic equation of the form:
$a {x}^{2} + b x + c = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Which can give two roots due to the $\pm$square root.

Solution

$y = - {x}^{2} + 0 x + 2$

for roots, $y = 0$

$- {x}^{2} + 0 x + 2 = 0$

$a = - 1 , b = 0 , c = 2$

so

$x = \frac{\pm \sqrt{8}}{- 2} = \pm \sqrt{2}$

$x = \sqrt{2}$

or

$x = - \sqrt{2}$